Question

Find the derivative of the vector function

r ( t ) = ta x ( b + tc )

Short answer

The derivative of the vector function is

\(r'(t) = ab + 2act\)

Step-by-step solution

Step 1: Applied the derivative function

Use the formula for derivative

\(\frac{d}{{dx}} = (f(x)g(x)) = f(x)g'(x) + f'(x)g(x)\)

Step 2: Solution of the vector function

Let’s applied the formula

\(\begin{array}{l}\frac{{d(ta(b + tc))}}{{dt}} = ta(b + tc)' + (ta)'(b + tc)\\r'(t) = ab + 2act\end{array}\)